What is the solution for 9xy^'=2xe^x-9y+6x^2 ?

The solution for 9xy^'=2xe^x-9y+6x^2 is y=(2(e^xx-e^x)}{9x}+\frac{2x^2)/9+(c_{1})/x

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9xy^'=2xe^x-9y+6x^2

9 x y^{^{'}} = 2 x e^{x} - 9 y + 6 x^{2}

y = \frac{2 ( e ^{x} x - e ^{x} )}{9 x} + \frac{2 x ^{2}}{9} + \frac{c _{1}}{x}

Solution steps

9 x y^{'} (x) = 2 x e^{x} - 9 y + 6 x^{2}

Solve linear ODE:

y = \frac{2 ( e ^{x} x - e ^{x} )}{9 x} + \frac{2 x ^{2}}{9} + \frac{c _{1}}{x}

y = \frac{2 ( e ^{x} x - e ^{x} )}{9 x} + \frac{2 x ^{2}}{9} + \frac{c _{1}}{x}

\frac{2 s + 6}{s ^{2} + 4}

x^{4} + 5 y^{4} x^{5} + 4 y^{^{'}} = 0

\frac{1}{3 s - 2}

\frac{e ^{x}}{1 - x}

\int (x^{2} + 1) e^{- 2 x} d x

What is the solution for 9xy^'=2xe^x-9y+6x^2 ?
The solution for 9xy^'=2xe^x-9y+6x^2 is y=(2(e^xx-e^x)}{9x}+\frac{2x^2)/9+(c_{1})/x